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Argument of a complex number z = x + iy having x = -y where y is a positive number is1. 45°2. 135°3. 225°4. 315°

Answer» Correct Answer - Option 2 : 135°

Concept:

The argument of a complex number z = x + iy

arg(z) = tan-1\(\rm \left(y\over x\right)\)

The angle is according to the sign of the y and x

  • Both positive then angle ∈ [0°, 90°]
  • Negative x and positive y then angle ∈ [90°, 180°]

 

Calculation:

Let the complex number be z = x + iy

arg(z) = tan-1\(\rm \left(y\over x\right)\)

∵ y > 0 and x = -y

arg(z) = tan-1\(\rm \left(y\over (-y)\right)\)

arg(z) = tan-1(-1)

arg(z) = 135° (∵ Negative x and positive y then angle ∈ [90°, 180°])


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